Alphametics, the SAT and the theory behind math tests

I once saw an alphametic in an SAT question -- simpler than this one but with the same basic principle. My first thought (after, "Was that an alphametic?") was what a great question.

Of course, solving alphmetics is a completely useless skill. No one has ever or will ever actually needed to do one of these. It is that very frivolousness that makes it such a good question for a college entrance exam. It requires sophisticated mathematical reasoning but it comes in a form almost none of the students will have seen before.

For comparison, consider a problem you would not see on the SAT*, factoring a trinomial that wasn't the square of a binomial (this is another skill you'll never actually need but it's not a bad way for students to get a feel for working with polynomials). Let's look a two students who got the problem right:

Student one hasn't taken algebra since junior high but understands the fundamental relationships, finds the correct answer by multiplying out the possibilities;

Student two was recently taught an algorithm for factoring, doesn't really understand the foundation but is able to grind out the right answer.

Obviously, we have a confounding problem here, and a fairly common one at that. We would like to identify understanding and long term retention but these can easily be confused with familiarity with recently presented information (particularly when certain teachers bend their schedules and curricula out of shape to teach to the test). The people behind SAT have partly addressed this confounding by including puzzle-type questions that most students would be unfamiliar with.**

All too often, the people behind other standardized tests deal with the issue by pretending it doesn't exist.




* Not to be confused with the SAT II, which is a different and less interesting test.

** The type of kid who reads Martin Gardner books for recreation would generally do fine on the SAT even without the familiarity factor (though the prom may not go as well).

Battered Party Syndrome?

Joseph and I generally try to avoid being overly political in this forum but just in terms of behavioral science, the following question is going to bother me all day.

Have the Democrats actually reached the stage where they will refuse to take an overwhelmingly popular position because, when they win, it makes the Republicans mad?

An alphametic pre-footnote

Light posting today, but since I'll be mentioning alphametics in an upcoming post I thought I'd give you something to chew on while you're waiting.

In 1924, the great Henry Dudeney published the following puzzle in the Strand Magazine:

S E N D

+ M O R E
__________________

M O N E Y

Each letter here represents a digit 0 through 9. If you substitute in the proper digits, the first two numbers (words) should add up to the third.

No one who reads this blog should have any trouble with this, but if you do, Wikipedia has a good step-by-step solution (though it does assume a passing acquaintance with number theory).

One more while we're on the subject

Though my recent posts on the subject have been a bit one-sided, I have to share my favorite example of copyrights being used to suppress (or at least attempt to suppress) creative output.

In 1994, Saul Zaentz, the man who had acquired the rights to the music of Credence Clearwater Revival sued John Fogerty for plagiarism because a song on Fogerty's latest album (which Fogerty wrote, played and sang) sounded like a CCR song (which Fogerty also wrote, played and sang). In other words an artist was basically sued for sounding like himself.

Zaentz lost and had to pay the court costs, but if Fogerty hadn't been a famous rock star with a new hit record on Warner Bros., how for do you think he would have gotten?

Intellectual Property and Monopsony

Joseph and I seem to be on a binge (purge?) of intellectual property posts, collecting piles of facts and observations on the subject. Somewhere in one of those piles we need to make room for the concept of monopsony.

From Wikipedia:

In economics, a monopsony (from Ancient Greek μόνος (monos) "single" + ὀψωνία (opsōnia) "purchase") is a market form in which only one buyer faces many sellers. It is an example of imperfect competition, similar to a monopoly, in which only one seller faces many buyers. As the only purchaser of a good or service, the "monopsonist" may dictate terms to its suppliers in the same manner that a monopolist controls the market for its buyers.

In entertainment, the norm is to have a huge number of artists trying to sell their products or services to a small number of buyers. Not only are there few buyers but access to these buyers is tightly controlled. The result can be an effective monopsony.

The results can look like this:

CrazySexyCool eventually sold over 11 million copies in the US, and became one of the first albums to ever receive a diamond certification from the RIAA,^[12] and won a 1996 Grammy Award for Best R&B Album and a 1996 Grammy Award for Best R&B Performance by a Duo or Group for "Creep".^[6] However, in the midst of their apparent success, the members of TLC filed for Chapter 11 bankruptcy on July 3, 1995.^[16]

They declared debts totaling 3.5 million dollars, ... the primary reason being that each member of the group was taking home less than $35,000 a year after paying managers, producers, expenses, and taxes.

Here the New York Times spells out some of those expenses:

The arithmetic is simple and sobering for aspiring stars: The average wholesale price of compact discs and cassettes is about $8 a unit. Thus, an artist with a 12 percent royalty rate, which is typical, gets about 96 cents per unit, or $480,000 on a "gold" record. From that, the record label recoups a portion of its advances to the artist for recording costs, music video production, tour support, independent promotional efforts, limousine services and so forth -- often as much as $170,000.

In other words TLC, which was only getting a seven percent royalty rate, was paying for pretty much everything, including a million or so just for the video for "Waterfalls."

The history of popular entertainment is filled with examples of creators selling million (sometimes multimillion) dollar properties for the equivalent of kind words and PEZ. This is not something you find in an efficient market.

A very good point

Tyler Cowen has a very good point:

Social Security offers cash benefits, whereas Medicare is an in-kind benefit, in the form of health care (which in turn is distinct from health, itself another in-kind benefit). Therefore always cut Medicare first.

That's all.

I think there may be come cases where this view is incorrect on the margins. But as a general principle it should be front and center in the public debate (especially given that, at the moment, the two programs are roughly equal in cost).

After all, treatment for medical conditions is nice but basic food and shelter might be preferable, if one can only have one of the two. If one can have both that is obviously better but it is worth noting Paul Krugman's point on which program has sounder finances going forward.

Other degrees of patent protection

Mark has a very interesting post on the length of copyright of intellectual property. I thought that I would compare these laws (which appear to give nearly 100 years of protection) to those for pharmacuetical drugs. From wikipedia:

In the US, drug patents give twenty years of protection, but they are applied for before clinical trials begin, so the effective life of a drug patent tends to be between seven and twelve years.

Medications have enormous development costs, the low end of the estimates are $100 to $200 million dollars (the cost of the clinical trials, alone, is enormous). Yet we are content to give them an effective period of copyright of seven to twelve years.

This is an area of copyright law where we have attempted to balance the need to reimburse development costs with the value of allowing an innovation into the open market. Why do we see laws that are so much stricter with ideas like "Mickey Mouse" and "Superhero"?

It is certainly food for thought!

Alice in Lawyerland: would the laws Disney lobbied for have prevented Disney from existing in the first place?

(disclaimer: I have cashed a number of royalties checks over the years so the following is obviously not an attack on the concept of intellectual property. I like royalty checks. I'm just worried about the consequences of taking these things to an extreme.)

In 1998, the Walt Disney company had a problem: their company mascot was turning 70. Mickey Mouse had debuted in 1928's "Mickey Mouse In Plane Crazy" which meant that unless something was done, Mickey would enter the public domain within a decade. This was a job for lobbyists, lots of lobbyists.

From Wikipedia:

The Copyright Term Extension Act (CTEA) of 1998 extended copyright terms in the United States by 20 years. Since the Copyright Act of 1976, copyright would last for the life of the author plus 50 years, or 75 years for a work of corporate authorship. The Act extended these terms to life of the author plus 70 years and for works of corporate authorship to 120 years after creation or 95 years after publication, whichever endpoint is earlier. Copyright protection for works published prior to January 1, 1978, was increased by 20 years to a total of 95 years from their publication date.

This law, also known as the Sonny Bono Copyright Term Extension Act, Sonny Bono Act, or pejoratively as the Mickey Mouse Protection Act,[2] effectively "froze" the advancement date of the public domain in the United States for works covered by the older fixed term copyright rules. Under this Act, additional works made in 1923 or afterwards that were still copyrighted in 1998 will not enter the public domain until 2019 or afterward (depending on the date of the product) unless the owner of the copyright releases them into the public domain prior to that or if the copyright gets extended again. Unlike copyright extension legislation in the European Union, the Sonny Bono Act did not revive copyrights that had already expired. The Act did extend the terms of protection set for works that were already copyrighted, and is retroactive in that sense.

Mickey had been Disney's biggest hit but he wasn't their first. The studio had established itself with a series of comedies in the early Twenties about a live-action little girl named Alice who found herself in an animated wonderland. In case anyone missed the connection, the debut was actually called "Alice's Wonderland." The Alice Comedies were the series that allowed Disney to leave Kansas and set up his Hollywood studio.

For context, Lewis Carroll published the Alice books, Wonderland and Through the Looking Glass, in 1865 and 1871 and died in 1898. Even under the law that preceded the Mouse Protection Act, Alice would have been the property of Carroll's estate and "Alice's Wonderland" was a far more clear-cut example of infringement than were many of the cases Disney has pursued over the years.

In other words, if present laws and attitudes about intellectual property had been around in the Twenties, the company that lobbied hardest for them might never have existed.

There's nothing unusual about a small company or start-up exploiting lapsed or unenforced copyrights to get a foothold. The public domain has long been fertile ground for stage companies, record companies, publishers, and producers of movies or radio and television; it's just been getting a lot less fertile lately.

Instrumental Variables

Reading this post by Andrew Gelman got me thinking: how do we really know if a variable is an instrument? Demonstrating that a variable is an instrument often seems to be a matter of telling a compelling clinical story but leaves one with strong and unverifiable assumptions.

This is a real issue with the Physician Preference instrument in pharmacoepidemiology where it has the potential to be either a major advance or a blind alley. But how would one know for sure? I suspect that it is more likely the former than the latter but sorting this out with any level of certainty isn't easy.

Any insights out there?

Study: Teacher bonuses don't affect student tests

from the AP:

ATLANTA – A study released Tuesday found that offering performance bonuses to teachers does nothing to raise test scores, raising doubts about the viability of the Obama administration's push for merit pay to improve education.

The study released Tuesday by Vanderbilt University's National Center on Performance Incentives researchers found that students in classrooms where teachers received bonuses saw the same gains as the classes where educators got no incentive.

"I think most people agree today that the current way in which we compensate teachers is broken," said Matthew Springer, executive director of the Vanderbilt center and lead researcher on the study. "But we don't know what the better way is yet."

The ultimate superpower is litigation

As part of our ongoing series on the surreal world of intellectual property (see the last post), here's a fun fact from comic book writer and historian Don Markstein:

Marvel and DC Comics are arch-rivals when it comes to market share in the comic book industry. But they're capable of an amazing degree of cooperation when it comes to maintaining their shared position as the industry's leaders. One of the ways they cooperate is in maintaining a joint trademark on the word "superhero" — as if Charlton, Harvey, Archie, ACG and Gold Key, to name only a few of the dozens that used both the genre and the word back before they established their mutual legal hegemony over it, never existed — to say nothing of Dark Horse, Image and others that use the genre today and aren't permitted to use the word.

In fact, here's a Dell comic book that actually made the term its very title, long before Marvel and DC decided to sew up rights to it. This should serve as a beacon to anyone willing to attempt to withstand the mighty onslaught of their lawyers, and point out that the word was in general use, with nobody even attempting to prevent others' using it, even before Superman.

Graph of the Day -- Copyrights

From Wikipedia:

I'll have more on this later.

Murphy strikes again

If you have ever wondered what else could go wrong, this is a great example.

What makes it tricky is how many different sets of rights need to be balanced. Clearly tenants need time to be able to move. It's obvious that owners need to be able to sell if ownership is to have any real meaning. And the new owners need to be able to actually take possession of their property. But somehow an outcome has happened that is sub-optimal for all involved.

What is it about real estate that makes it a locus of difficult transactions?

Today's Napoleon quote

In handy comics form:

"Heroin's doing the heavy lifting"

I'm pretty sure I'll quote this some time in the near future.


From Kumail Nanjiani:



I first heard this on This America Life. If you enjoyed it, go by and give them a buck. They're good people.